Reggie bought bottles of pomegranate syrup, peach syrup and dragonfruit syrup of 200 mℓ, 300 mℓ and 150 mℓ respectively. He counted to pour them into smaller cups of equal amount with no leftover.
- What was the largest possible amount of syrup in each cup?
- How many cups of syrup of pomegranate syrup, peach syrup and dragonfruit syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)
(a)
Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Highest common factor of 200 mℓ, 300 mℓ and 150 mℓ = 50 mℓ
So, 50 mℓ is the largest possible amount of syrup in each cup.
(b)
Number of cups of pomegranate syrup
= 200 ÷ 50
= 4
Number of cups of peach syrup
= 300 ÷ 50
= 6
Number of cups of dragonfruit syrup
= 150 ÷ 50
= 3
Reggie would have 4 cups of pomegranate syrup, 6 cups of peach syrup, 3 cups of dragonfruit syrup
Answer(s): (a) 50 mℓ; (b) 4, 6, 3